PEOF. W. M. HICKS: A CEITICAL STUDY OF SPECTRAL SERIES. 75 



are not necessarily one-half of (477) and +(407). The variations given are the 

 greatest allowable subject to observational errors alone, and the assumed value for N, 

 but that they should be so great as these must be regarded as highly improbable. 

 The variations for KP are so large because the constants are determined from 

 P(2.3.4) instead of P (1.2.3), a less accurate value of P(l) being more effective for 

 correct determination of /x or a than a more accurate one of P (2). Two estimates are 

 inserted for RbP (which were deduced from P (1.2.3)), the larger are based on K.R.'s 

 estimates of possible error, the smaller on L.'s estimate of probable error ;. the truth 

 probably lies between the two. Different positive and negative errors appear under 

 RbS and KD. This is due to the fact that small permissible errors were introduced 

 into the observations giving the constants in- order to bring all the calculated series 

 within limits. The values of v inserted in the table give the values used in correcting 

 the two sharp series to a constant v. They are not the same as those given elsewhere 

 as the most probable values, but as they were used in the original calculations, and as 

 nothing was to be gained by recalculating, they are left as they were. 



The first column under each series gives the value of the limit A ; the top number 

 being its value and the lower the value of the D when it is written in the form N/D 2 . 



ThusmNaP P(oo) = 41446761'69 = N/(l'626740 + '000033) 2 . 



The third line under P gives the values for P 2 on the supposition that 

 P 2 (oo) = P^oo). The top number in the second column gives the value of /A and 

 the lower the value of the denominator when m = 1, i.e., the value of I+/A + M. Thus 

 in NaPj 



H = 1-1 48678 '000477 and the denominator of P : (l) = 2 -11 6902 '000070. 



The variations are, of course, subject to the correct value of N being 109675 and to 

 m being integral. Alterations in N or taking, say, m to be m+'o would produce 

 further consequent alterations in A. 



Relation (D). An inspection of the values given for S ( oo) and D ( oo), with their 

 possible variations, show that in all cases their values are the same within limits of 

 observation. 



Relation (E). The equality of P t ( oo ) and P 2 ( co ) is so far justified by the fact 

 that its assumption in calculating P 2 gives constants which reproduce the observations 

 within possible errors. There is. however, still room for doubt as to exact equality, 

 owing to imperfection of data. 



Relation (F). Viz. : S ( oo ) = VP (1). If S ( oo ) be written in the form N/D' 2 and 

 D be the denominator of P(l), this relation involves the equality of D and D'. The 

 values are given in the table. From them we get the following values of D' D : 



Na. . . '000084 '000235 Rb . . . '000581 -'000624 \ 



K . . . '000656 + -001217 +'000569 J 



Cs , . . '000324+ ? 

 L 2 



